firewood harvest from forests of the murray-darling basin, australia. part 1: long-term, sustainable...

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Firewood harvest from forests of the Murray-Darling Basin,Australia. Part 1: Long-term, sustainable supply availablefrom native forests

P.W. Westa,b, E.M. Cawseyc,�, J. Stolc, D. Freudenbergerd

aSchool of Environmental Science and Management, Southern Cross University, Lismore, NSW 2480, AustraliabSciWest Consulting, 16 Windsor Court, Goonellabah, NSW 2480, AustraliacCSIRO Sustainable Ecosystems, GPO Box 284, Canberra, ACT 2601, AustraliadGreening Australia, PO Box 74, Yarralumla, ACT 2600, Australia

a r t i c l e i n f o

Article history:

Received 5 February 2008

Accepted 29 February 2008

Available online 18 April 2008

Keywords:

Firewood

Murray-Darling basin

Eucalypt

Silviculture

Sustained yield

Biodiversity

nt matter & 2008 Publishioe.2008.02.017

hor. Tel.: +61 2 6242 1628;[email protected]

a b s t r a c t

The Murray-Darling Basin is a 1 million km2 agricultural region of south-eastern Australia,

although 29% of it retains native forests. Some are mallee eucalypt types, whilst the

‘principal’ types are dominated mainly by other eucalypt species. One-third of the 6–7

million oven-dry tonne of firewood burnt annually in Australia is obtained from these

forests, principally through collection of coarse woody debris. There are fears that removal

of this debris may prejudice the floral and faunal biodiversity of the Basin. The present

work considers what silvicultural management practices will allow the long-term

maintenance of the native forests of the Basin and their continued contribution to its

biodiversity. It then estimates that the maximum, long-term, annual, sustainable yield of

firewood which could be harvested, by collection of coarse woody debris, from principal

forest types of the Basin would be 10 million oven-dry tonne yr�1. An alternative, harvest of

firewood from live trees by thinning the principal forests and clear-felling mallee forests,

would be able to supply 2.3 million tonne yr�1 sustainably. Whilst coarse woody debris

harvests could supply far more than the present demand for firewood from the Basin, they

would lead to substantial reductions of the debris remaining in the forests; this may be

detrimental to biodiversity maintenance. Live tree harvest does not lead to this problem,

but would barely be able to supply existing firewood demand.

& 2008 Published by Elsevier Ltd.

1. Introduction

The Murray-Darling Basin is the catchment for the largest

river drainage system of Australia. Its total area is 1 M km2,

occupying most of inland, south-eastern, mainland Australia.

Environmental conditions vary widely across the Basin,

particularly as rainfall declines from more than 1000 mm yr�1

in its most easterly and southerly parts to less than 300 mm

yr�1 towards the arid, interior of the continent; about 75% of

ed by Elsevier Ltd.

fax: +61 2 6242 1688.u (E.M. Cawsey).

the Basin has a rainfall of less than 750 mm yr�1. Over the last

200 yr, large areas of the Basin have been cleared for

agriculture; it now produces wheat, rice, cotton, sheep, cattle

and horticultural products. In the wetter regions of the south-

eastern Basin, large areas of exotic softwood (Pinus radiata)

plantation forests have been established. Only small areas

have been established with hardwood plantations.

Native forests remain over at least 29% of the area of the

Basin. These forests have been classified and mapped by the

dx.doi.org/10.1016/j.biombioe.2008.02.017

mailto:[email protected]

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B I O M A S S A N D B I O E N E R G Y 3 2 ( 2 0 0 8 ) 1 2 0 6 – 1 2 1 9 1207

National Forest Inventory of Australia [1], based on a

classification system described by Specht and Specht [2] and

Specht et al. [3]. Along the wetter eastern and southern

fringes of the Basin are small areas of ‘tall’ (mature height

430 m), ‘open’ (crowns cover 50–80% of the ground surface)

forest. Moving progressively towards the arid interior of the

continent, the forests grade through ‘medium’ (mature height

11–30 m) and ‘low’ (2–10 m), open forests to medium and low

‘woodlands’ (crowns cover 20–50% of the ground surface).

Both single- and multi-aged forests occur. Some are mono-

specific and others contain a mixture of tree species. The

more complex types, multi-aged and/or mixed-species for-

ests, are most common.

About 9% of the native forest area consists of mallee

eucalypt types (small, multi-stemmed eucalypt species of low

mature height). About 71% is of other eucalypt types, the

dominant species varying with height and openness of the

forest. The remaining 20% of the forests are dominated by one

or other species of the genera Acacia, Callitris, Casuarina or

Melaleuca; often these species occur in mixture with euca-

lypts. The non-mallee eucalypt types, together with the

forests dominated by other genera, will be considered

together here and termed the ‘principal’ forest types of the

Basin. By far, non-mallee eucalypt forests of medium height

are the most common forest type, constituting 66% of the

total area of native forests of the Basin. Fig. 1 shows an

example of this type of forest.

The productivity of the forests of the Basin is much lower

generally than that of the taller, native forests in the higher

rainfall areas of the eastern and southern coastal regions of

Australia. The only native forests of the Basin which have

been used consistently for commercial timber production are

Fig. 1 – An example of a mature stand of non-mallee,

medium height, open eucalypt forest of the Murray-Darling

Basin. Forests with this structure are the most common

native forest type throughout the Basin. This stand

regenerated more than 100 yr ago, after all trees on the site

were killed by ringbarking (girdling). It was used for animal

grazing subsequently. It contains a mixture of Eucalyptus

rossii, Eucalyptus mannifera and Eucalyptus macrorhyncha.

those of White Cypress Pine (Callitris glaucophylla), which are

widespread over the Basin, River Red Gum (Eucalyptus

camaldulensis), which is widespread over the Basin but

confined to riparian areas and some ‘ash’ eucalypt forests

(usually Alpine Ash, Eucalyptus delegatensis), which are located

in higher rainfall and higher altitude areas along the south-

eastern fringe of the Basin. Together, these provide only a very

small proportion of the timber produced commercially from

Australian native forests.

In [4] it was estimated that 6–7 M t of firewood (all firewood

amounts referred to in this paper are oven-dry weights) are

burnt annually in Australia, the bulk for domestic heating.

About 2–2.5 M t of this are obtained from the native forests of

the Basin, mostly from privately owned forests.

Some of the mallee eucalypt woodlands of the Basin

(including species such as Eucalyptus socialis, Eucalyptus

gracilis, Eucalyptus oleosa subsp. oleosa and Eucalyptus dumosa)

have been harvested consistently for firewood (often during

land clearing). Sometimes the large lignotuberous mass at the

base of the stem of these species, from which coppice arises,

is used as firewood and sometimes the stem wood is used.

Large amounts of firewood are obtained also from the

principal native forests of the Basin. Most of this is collected

as fallen, coarse woody debris, although some may be

obtained during land clearing or by felling live trees. Concern

was expressed in [4] that the removal of this debris may have

important consequences for the biodiversity of the Basin. It

was suggested that ‘[o]f particular concern are probable

effects on ecosystem processes such as nutrient cycling and

plant establishment, because of the potential loss of highly

specialised species of invertebrates and fungi.’ As well, it was

believed that loss of coarse woody debris might deprive some

faunal species of their habitat.

The present work establishes a basis for responsible

management of the privately owned, native forests of the

Basin, which are appropriate for firewood harvest. It is

assumed that the objective of management is to ensure

firewood harvesting can continue, whilst conserving the

forests and maintaining, or hopefully increasing, their con-

tribution to the overall biodiversity of the region. The

consequences are examined of both the continuation of

firewood harvesting of coarse woody debris and of an

alternative, where firewood is obtained by felling live trees.

For each alternative, estimates are made of the maximum,

long-term, sustainable yield of firewood which might be

obtained from these forests: in this context, maximum

sustainable yield means removal of firewood at a rate equal

to its rate of replacement by growth of forests. As well,

estimates are made of the amounts of coarse woody debris

which will remain in the forests in the long-term, if firewood

is harvested at the maximum, long-term, sustainable rates.

2. Approach

There are well developed methods available to determine how

a large and complex forest area should be managed to ensure

a long-term, sustainable supply of the ‘products’ which can

be obtained from it (e.g. [5,6]). The approach taken here

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followed the steps given in [7], which involve:

�

Tpc

Ft

P

P

P

P

M

T

a

Determination of the total area of the forest and stratifica-

tion of that area by those characteristics which are likely to

affect its ability to supply the products (characteristics

such as forest type, age or productive capacity).

�
Choice of a set of possible silvicultural management
regimes which could be applied to produce the products,

in any stand of any particular stratum.

�
Application of a forest growth and yield modelling system
to predict the amounts of the products available from any

stand in the forest, at any time in the future and when any

particular management regime is applied to it.

�
Use of the information from the three preceding steps to
determine what areas of which strata of the entire forest

area should be managed, with which of the possible

silvicultural management regimes, to achieve a long-term,

sustainable supply of the products (usually annually) from

the entire forest area. As well, an estimate of the sustain-

able supply is obtained. This last step often involves

application of a mathematical programming system.

In the present work, only a single forest product, firewood,

will be considered. The next four sections describe how each

of these four steps was implemented here.

3. Forest area and stratification

GIS surfaces of the Murray-Darling Basin were obtained

showing forest cover, forest type and land tenure (National

Forest Inventory, Bureau of Rural Sciences, Australia), digital

elevations, urban areas and water courses (Geosciences

Australia) and land productive capacity (Dr. D. Barrett, CSIRO

Plant Industry, Australia). The measure of productive capacity

was the maximum annual rate of net primary production of

vegetation at a site, referred to here as ‘NPP index’; this is

described in more detail in Appendix A. Over the entire Basin,

the index varied over the range 0.3–14 t ha�1 yr�1.

able 1 – Areas of principal forest types and mallee eucalypt froductive capacity (NPP index) classes, determined as beingollection of coarse woody debris or by thinning live trees

orestype

Site productive capacityclass number

NPP index class(t ha�1 yr�1)

Av

rincipal 1 0.2–3.2




allee – 0.4–11.2

otal

rea

This information was used to compile a map of the Basin

showing the privately owned (or leased) forest areas from

which it might be appropriate to obtain firewood by collection

of coarse woody debris. Public lands were excluded; firewood

supply from these areas is actively regulated by the relevant

state agencies and most firewood comes from privately

managed land [4]. Areas further than 500 km from a capital

city were excluded; the main market for firewood is in the

capital cities and it was considered economically unfeasible

to transport firewood further than this. Mallee forests were

also excluded; they contain negligible amounts of coarse

woody debris. These areas were then stratified into four site

productive capacity classes, defined by NPP index (Table 1)

and by 1-yr age classes (age was defined as the time since the

forest regenerated from bare ground following clearing,

destructive wildfire or other natural calamity). Little informa-

tion was available about forest age to do this reliably.

However, it is believed [8] that a large proportion of the

forests of the Basin regenerated around the turn of the 20th

century, followed by a second period of regeneration in the

1950s. Given this, and from observations by the present

authors of the forests of the Basin, it was assumed that in

2004, 40% of their area would be aged 50–60 yr, 50% would be

100–120 yr and 10% would be 150–178 yr. It was assumed that

forest areas were distributed evenly in each annual age class

across these three periods.

This resulted in a map with an area of 12.3 M ha of principal

forest types, subdivided into 244 site productive capacity� -

age class strata, which could be considered potentially

suitable for firewood harvest by coarse woody debris collec-

tion. Table 1 lists the areas of these forests in each of the four

site productive capacity classes. Fig. 2(a) shows a map of their

distribution across the Basin.

As discussed in more detail later, both principal and mallee

eucalypt forest types can be considered appropriate for

firewood harvests by removing live trees. However, the

logging machinery used to do this would cause much greater

site disturbance than would firewood collection from coarse

woody debris. Accordingly, some additional constraints were

orest types of the Murray-Darling Basin, in various siteappropriate to consider for firewood harvesting, either by

erage NPP index forclass (t ha�1 yr�1)

Area appropriate for firewoodharvesting by different methods

(M ha)

Coarse woodydebris collection

Removal oflive trees

1.9 2.9 2.1

3.4 3.1 2.1

4.9 3.1 2.3

8.3 3.1 2.2

1.2 – 1.1

12.3 9.8

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Fig. 2 – Distribution of forest areas across the Murray-Darling Basin considered appropriate for firewood harvesting.

(a) Principal forest type areas appropriate for harvesting by collection of coarse woody debris only. (b) Principal forest type and

mallee eucalypt areas appropriate for harvesting by removing live trees.


imposed to determine areas of the Basin potentially suitable

to obtain firewood by harvesting live trees. Forest areas with a

slope of 151 or more were excluded, to avoid any possibility of

post-logging soil erosion and the expense and difficulty of

logging steeper slopes. To avoid prejudicing faunal biodiver-

sity through logging, forest areas were excluded where

clearing had reduced forest cover in the landscape generally

to less than 30%, or which were riparian areas within 50 m of

streams or rivers or which were remnant forests with an area

of less than 100 ha.

With these additional exclusions from the previously

determined 12.3 M ha of principle forest types and with the

inclusion of mallee types, a total of 9.8 M ha of forest, 8.7 M ha

of principal forests and 1.1 M ha of mallee forests, then

remained as being potentially suitable for firewood harvesting

by removal of live trees. These were subdivided into 305 site

productive capacity�age class strata. Table 1 lists the areas of

these forests in different site productive capacity classes.

Note that all the mallee forests are located in areas of

relatively low productive capacity in the Basin; 95% of their

total area has an NPP index below 2 t ha�1 yr�1. Accordingly,

all mallee forests were assigned to a single site productive

capacity class stratum. The distribution across the Basin of

these forests is shown in Fig. 2(b).

4. Silvicultural management

The principal consideration in deciding how forests of the

Basin should be managed for firewood production was that

they should continue, and if possible increase, their contribu-

tion to the overall ecological biodiversity of the Basin. With this

in mind, a standard management regime was developed for

harvesting firewood (a) through coarse woody debris collection

from principal forest types, (b) through harvesting live trees by

thinning principal forests or (c) through harvesting live trees

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from mallee forests. These regimes specify at what stages

during the life of any stand, harvests should occur and what

quantities of firewood should be removed at each harvest.

The overall objective of the present work is to determine

the maximum long-term, steady, sustainable supply of fire-

wood available from the Basin in any calendar year in the

future. Because of variations of site productive capacity and

the uneven distribution of age classes of forests across the

Basin, it will inevitably be impossible to apply the standard

management regime in each and every forest stand across the

Basin to achieve this steady, sustainable yield. In some

calendar years, harvests, which might be due under the

standard regimes, may have to be delayed in some stands, or

brought forward to an earlier year, or even not done at all.

That is, some variations about the standard regimes will have

to be allowed. Determination of how these variations should

be applied is a basic problem faced by any forest manager

responsible for maintaining a long-term, sustainable supply

of forest products from a large, complex forest area.

Sections 4.1–4.3 describe the standard management re-

gimes developed here and the variations from them which

were considered appropriate.

4.1. Coarse woody debris collection in principal foresttypes

Collection of coarse woody debris for firewood is a relatively

benign harvest practice. It causes only minor site disturbance,

principally from vehicle access. It has no effect on the

subsequent growth behaviour of the live trees in the forest.

However, it does affect the amount of woody debris remain-

ing in the forest for maintenance of biodiversity, an issue

discussed in more detail later.

For the ‘standard’ management regime for coarse woody

debris harvest in principal forest types, it was first assumed

that the forest would grow to 178 yr of age on average, the age

which was determined as the average lifespan of forests of

the Basin [9]. After that, it was assumed the forest would be

destroyed by fire, or other natural calamity, and would

regenerate anew. The standard regime then allows collection,

at any stage of development of the stand, of as much as

possible of the firewood available from its coarse woody

debris, with the following constraints:

�
No harvest would be done unless it yielded at least
1.5 t ha�1 of firewood; this was considered the minimum

amount that would be worthwhile collecting commer-

cially.

�
The first harvest in any stand would take place around
20–25 yr of age, by which time the stand should be well

developed.

�
To avoid too frequent intervention in a stand, subsequent
harvests should be done at intervals of 5–10 yr, or delayed

further until 1.5 t ha�1 of firewood became available.

�
No harvests would take place after 178 yr of age, if the
stand lived beyond that age.

Seven possible variations of this standard regime were

considered appropriate for any particular stand. The first

possibility was that there was no firewood harvest at all from

the stand. The other six possibilities were simply random

variations of the standard regime. The lifetime for the stand

was selected randomly, within the range 161–195 yr of age.

The age at which the first harvest was done was chosen

randomly from within the range 20–25 yr. The number of

harvests to be done in each rotation was chosen randomly

within the range 20–40. The harvests were then assumed to

be spaced at approximately equal time intervals. However,

the exact timing of any harvest was chosen randomly within

71 yr of the time of exactly equal spacing of harvests, subject

only to delaying any harvest until at least 1.5 t ha�1 of

firewood was available from it.

4.2. Removal of live trees by thinning principal foresttypes

Based on the work of Florence [10], it appeared that the most

appropriate ‘standard’ management regime for thinning

these forests should involve ‘flexible selection practice’ [10,

p. 229]. In Florence’s words this is a ‘regime which aims to

meet a number of objectives, and can result in, or maintain a

highly variable structure. It may take account of both short-

and long-term supplies of wood and, at the same time,

maintain, on environmental grounds, a good level of ecolo-

gical, structural and aesthetic diversity throughout the forest.’

Such a regime is consistent with the present objectives of

producing firewood yields and ensuring maintenance of the

biodiversity of the forest ecosystems of the Basin.

Our experience of the principal forest types of the Basin

suggested that flexible selection practice would involve

selection of trees for harvest at thinning with diameters at

breast height over bark in the range 15–60 cm. The trees

retained would be of good bole form and have canopies in a

suitable condition to allow them to respond to thinning by

accelerating their stem diameter growth rates; although it

was not the aim of the present work to consider the use of

forests of the Basin for wood products other than firewood, it

was assumed that silvicultural practices which might lead

eventually to production of higher value timber products

from trees of larger diameter might have long-term economic

advantage.

Trees with stems in excess of 60 cm diameter would be

retained at thinning, since it is these which provide hollows

important as faunal habitat (e.g. [11–14]), or may, in the

medium term, grow to a size such that they would do so.

Some regeneration would be expected to occur in these

forests after thinning, either as coppice or as seedlings from

natural seed shed; this will ensure maintenance of a high

level of structural diversity.

Insufficient is known presently of the growth dynamics of

the principal forest types of the Basin to prescribe with any

certainty what ages, intensities and frequencies of flexible

selection thinning would be most appropriate in them.

Experience of one forester familiar with them (A. Deane,

State Forests NSW, pers. comm.) suggested that up to three

thinnings might be appropriate in stands of 30–120 yr of age

growing on sites of higher productive capacity. Stands of

lower productive capacity might be thinned twice at most,

when aged 50–150 yr. Various studies of some of the less

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Table 2 – Standard thinning regimes, involving ‘flexibleselection’ practice, for principal forest types of variousproductive capacities (Table 1) in the Murray-DarlingBasin

Siteproductivecapacityclassnumber

Numberof

thinnings

Age rangewithin whichfirst thinningis done (yr)

Delay toeach

subsequentthinning

(yr)

1 2 50–60 30–60

2 2 50–60 30–60

3 3 30–40 40–45

4 3 30–40 40–45

All thinnings would involve removal of 50% of the basal area over

bark of the stand at the time of thinning.


productive forest types of Australia suggests that thinnings

which involve removal of up to 50% of the basal area over bark

of a stand should result in worthwhile acceleration of the

stem diameter growth rates of the retained trees. At the same

time, this intensity of thinning would not be so great that full

occupancy of the site is lost, with a consequent loss of overall

production by the stand [10, pp. 210–213; 15–17].

Given these various considerations, Table 2 shows the

standard thinning regime chosen here for stands of different

productive capacities of the principal forest types of the

Basin. When prescribing a standard regime for any particular

stand in later computations to determine sustainable fire-

wood yields, the age at which the first thinning was done and

the delay to each subsequent thinning were chosen at

random from within the ranges specified in Table 2. As in

Section 4.1, it was assumed that the lifetime of a stand would

be 178 yr of age, after which it would be destroyed by fire or

other natural calamity and would regenerate anew.

When determining long-term, sustainable firewood sup-

plies, the variations about the standard regime prescribed for

any stand were as follows. In each variation, the lifetime of

the stand was chosen randomly within the range 165–191 yr.

The first variation was simply that the stand should remain

unthinned throughout its life. Other variations used ran-

domly selected ages of first thinning and delays to subse-

quent thinnings, from the ranges specified in Table 2. Nine

such other variations were used for stands in site productive

capacity classes 1 and 2, whilst 14 were used for stands in site

productive capacity classes 3 and 4.

4.3. Removal of live trees from mallee forests

Very limited information is available about appropriate

silvicultural management practices for mallee forests of the

Basin. In [18], it was concluded that long-term maintenance

of the mallee ecosystem was best served by a clear-felling

harvest of live trees at 50 yr intervals. This would be followed

by coppice regeneration, which occurs reliably and leads

generally to development of even-aged regrowth stands.

A clear-felling harvest of any particular mallee forest stand,

at an age chosen randomly within the range 40–60 yr of age,

was considered here as its ‘standard’ management regime.

The variations considered about this regime were either that

it was not harvested or nine other variations, where it was

harvested at a different age, also chosen randomly within the

range 40–60 yr.

5. Growth and yield modelling

For the present work, a growth and yield model was

developed for the principal forest types of the Murray-Darling

Basin. This is described in Appendix A. The input required by

the model is the productive capacity of the site (as measured

by NPP index) on which a stand is growing and choices of

when harvests of firewood are to be done by coarse woody

debris and/or by removal of live trees at thinning. The

proportions of the available wood biomass (all plant biomass

amounts referred to in this paper are oven-dry weights) to be

removed at each harvest must be specified also. The model

then predicts, annually for stand ages up to 200 yr, the

amounts of firewood harvested and the amounts of coarse

woody debris and live tree biomass which remain in the

stand.

Using data collated in [18] for clear-felling mallee forests, a

model to predict firewood yields [B0MFðTÞ; t ha�1] at any age T

(yr) was determined as

B0MFðTÞ ¼ 8:91þ 0:274T; if To59, (1a)

and

B0MFðTÞ ¼ 25:1; if TX59. (1b)

6. Determining sustainable firewood yield

Central to the present work is the assumption that respon-

sible management will maintain the existing native forests of

the Basin and their contribution to its biodiversity. The

standard silvicultural regimes for firewood harvest and their

alternatives, as developed in Section 4, were designed to

ensure that these contributions could continue. Of course,

from time to time any particular forest area will reach the end

of its lifespan. To ensure its continued contribution to the

biodiversity of the Basin, it must be assumed that it will then

regenerate and replace itself.

The constraints imposed, both by the management regimes

and the growth rates of the forests, will limit the amount of

firewood which can be harvested. Given these constraints, it

is necessary to determine what combinations of the standard

and alternative silvicultural management regimes must

applied to what areas of the Basin to obtain a steady, annual,

sustainable supply of firewood from the Basin.

As mentioned in Section 2, mathematical programming

systems are used generally by forest managers to determine

both the level of the maximum, long-term, sustainable wood

supply and how the forest area should be managed to achieve

that supply. For the present work, a linear mathematical

programming system was devised to do this, as described in

Sections 6.1 and 6.2.

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6.1. Mathematical programming system

The ultimate objective of applying the mathematical pro-

gramming system is to estimate the maximum, long-term,

steady, sustainable annual supply of firewood (S, t yr�1), which

can be obtained from the privately owned native forests of the

Basin.

To determine S, a choice must first be made of the specific

period into the future over which the mathematical program-

ming system is to be applied, termed the ‘planning horizon’ of

the system. Suppose this is of length h yr. Suppose the total

area of forest to be harvested for firewood was subdivided

into s strata and the area (ha) of the ith stratum (i ¼ 1ys) was

Ai (ha). Suppose that ri alternative silvicultural management

regimes were considered as possibilities to apply to all or part

of the ith stratum. Suppose also that an area Aik (ha) of that

stratum was then actually managed with the kth (k ¼ 1yri) of

those options. Further, suppose that a weight Fijk (t ha�1) of

firewood was harvested from a stand in the ith stratum

(i ¼ 1ys), during the jth year of the planning horizon

(j ¼ 1yh), when treated with the kth possible management

regime (k ¼ 1yri).

The objective of the linear programming system was then

to determine what area of each stratum should be treated

with which of the silvicultural regime alternatives for that

stratum, to achieve the maximum possible supply of firewood

from the Basin, summed over the entire planning horizon.

That is, the objective function of the system was

MaximiseX

i

Xk

Aik

Xj

Fijk

0@

1A

24

35, (2)

where the Aik are the unknowns to be determined by the

system. Note that the summations in expression (2), and in

the equations below, are for i ¼ 1ys, j ¼ 1yh and k ¼ 1yri.

However, this maximum firewood supply was limited by

two constraints:

�
The sum of the areas treated with the various silvicultural
regime alternatives in any stratum must equal the total

area of that stratum. That is, there are s constraints in the

system of the form

Xk

Aik ¼ Ai ði ¼ 1 . . . sÞ. (3)

�
It is desired that the annual supply of firewood from the
entire Basin is to be constant at a steady annual amount of

S (t yr�1). However, it is unlikely that a solution will be

obtained to the system if the annual supply is constrained

to be exactly S. Rather, it was assumed that the supply in

any year should be within some (relatively small) propor-

tion (p) of S. This led to h constraints of the form

ð1þ pÞSXX

i

Xk

ðAikFijkÞXð1� pÞS ðj ¼ 1 . . .hÞ. (4)

In using this system, a value was guessed for both S and p. If

no solution for values of the Aik could then be found, a

smaller value of S or larger value of p was chosen and a

solution sought with those new values. Through a trial and

error process, the largest value of S and smallest value of p

were determined for which a solution to the system could be

obtained. Solutions to the system were determined using the

simplex method, as implemented in the MINOS suite of

computer programs, for solving large, complex, mathematical

programming problems [19,20].

6.2. Applying the mathematical programming system

For the present case, a planning horizon of 100 yr was used

(that is h ¼ 100), extending from the 1st of January 2004 until

the 31st December 2103. This was considered to be a length of

time reasonably foreseeable in human terms, both with

respect to the conservation of the forests of the Basin and

development of the firewood industry. The start of the

horizon, 2004, was determined by time at which the present

work was commissioned.

The system was applied twice, once to determine the

maximum, long-term, sustainable, annual supply of firewood

if harvesting involved only collection of coarse woody debris

from the principal forest types and a second time when

firewood was obtained only by felling live trees in both mallee

types and the principal forest types. In each case, the area of

forest to be harvested and its stratification, by site productive

capacity and age class, was as determined in Section 3 and

summarised in Table 1. The silvicultural management regime

options considered as possibilities in each stratum were the

standard regime and each of its alternatives, as discussed in

Section 4. The growth and yield modelling systems (Section 5)

were used to predict firewood harvest yields at any age during

the life of the stands in any one stratum. In applying the

growth and yield model for the principal forest types, it was

assumed that the productive capacity of the forest in any

particular stratum was the average NPP index for that class of

site productive capacity, as specified in Table 1; these class

averages were determined as weighted averages from the NPP

index GIS surface (Section 3), with weighting by the area

distribution of NPP index values across any NPP index class.

The age (Section 3) in 2004 of the forest of any stratum

determined its age at the start of the planning horizon. This

allows firewood harvest yields (the Fijk of the mathematical

programming system) from any stratum to be assigned to the

particular calendar year, during the planning horizon, in

which they are obtained. If the forest of a stratum reached the

end of its lifespan before the end of the planning horizon, it

was assumed to regenerate immediately and start a new

‘rotation’. The management regime option being considered

for the first rotation of that stratum was assumed to apply

also in subsequent rotations. Where firewood was being

harvested by thinning live trees from principal forest types,

any thinning which would have been due to be undertaken

before 2004 was assumed not to have been done.

7. Results

If firewood was harvested from coarse woody debris only

from the eligible principal forest types (Fig. 2a), its maximum,

long-term, sustainable supply was estimated as an average of

10.0 M t yr�1, which the supply constraints (4) ensured did not

vary annually outside the range 8.9–10.9 M t yr�1. This is far in

ARTICLE IN PRESS


excess of the 2–2.5 M t yr�1 of firewood it is believed is

harvested presently from the Basin [4].

When harvesting involved thinning live trees from princi-

pal forest types and clear-felling live trees from mallee

forests, over the areas shown in Fig. 2(b), the maximum,

long-term, sustainable supply was estimated as an average

of 2.3 M t yr�1, which did not vary annually outside the

range 2.1–2.5 M t yr�1. This is about equal to the present

harvest from the Basin. About 78% of this yield would

come from the principal forest types and the rest from mallee

types.

Fig. 3 shows estimates of the biomass of coarse woody

debris that would remain, on average over the entire

harvested areas, year by year over the planning horizon

when firewood was harvested at the maximum, long-term,

sustainable rates; the residual coarse woody debris quantities

were obtained as outputs from the model system at the same

time as firewood yields were determined. As might be

expected, when firewood is harvested by removing live trees

only, far greater amounts of coarse woody debris will remain

than when coarse woody debris is harvested.

With harvests from coarse woody debris only, the results in

Fig. 3 show that the average biomass of coarse woody debris

remaining over the 100 year planning horizon would be

3.0 t ha�1, varying from year to year in the range 2.5–3.7 t ha�1.

These results were averaged over all site productive capacities

across the Basin. In stands of particular productive capacities,

the amounts remaining would increase as productive capa-

city increased, typically from about 1.9 t ha�1 in stands of

productivity class 1 (Table 1) to about 3.3 t ha�1 in stands of

productivity class 4.

Fig. 3 – Average stand biomasses of residual coarse woody

debris, year by year over 2004–2103, after harvesting

firewood at the maximum, long-term, sustainable annual

rate from coarse woody debris of principal forest types only

(- - -), or by thinning live trees from principal forest types

and clear-felling mallee types (—), or if no firewood

harvesting was done at all (— - —). The results for each year

are averaged over the entire areas harvested by each of

these two methods (Fig. 2).

With harvests from live trees only, the average amount of

coarse woody debris remaining would average 17.6 t ha�1 over

the 100 yr, varying from year to year in the range 13.4–21.1 t

ha�1. Again, the residual amount would be higher in stands of

higher productive capacity, typically increasing from about

10.6 t ha�1 in stands of productivity class 1 to about 18.2 t ha�1

in stands of productivity class 4. The substantial decline in

the average amount of coarse woody debris remaining after

about 2050 is a consequence of the age distribution assumed

for the forests of the Basin (Section 3). Younger forests

contain smaller quantities of coarse woody debris; after

2050 the average age of the forests would decline as older

forests are lost through natural calamities and are replaced by

younger, regenerated forests.

Also shown in Fig. 3 is an estimate of how the average

amount of coarse woody debris across the Basin would vary

year by year if there was no harvesting of firewood at all. The

average over the 100 yr is 20.4 t ha�1, varying from year to year

in the range 16.2–23.4 t ha�1. These amounts are greater than

when firewood harvesting was done by live tree removal, even

though this involves no removal of coarse woody debris.

However, live tree removal by thinning reduces the stand

biomass of the live trees remaining in the forests. As evident

in model (11), the amount of coarse woody debris in a stand

increases with the biomass of the live trees in the stands;

hence removal of live trees from a stand leads to a decline in

quantities of coarse woody debris.

8. Discussion

It was estimated that a maximum annual supply of 10 M t yr�1

of firewood could be sustained over the next 100 yr by

harvesting coarse woody debris from the principal forest

types of the Murray-Darling Basin. This is far in excess of the

2–2.5 M t yr�1 believed to be harvested annually at present.

Harvesting this maximum amount would deplete substan-

tially the reserves of coarse woody debris in these forests

(Fig. 3). It remains to be established for forests of the Basin, or

indeed for forests of Australia generally, what quantities of

coarse woody debris need to be retained to ensure the

maintenance of the biodiversity of the flora and fauna of

these ecosystems. However, we believe that biodiversity

would certainly suffer if there was a decline in average coarse

woody debris across the forests of the Basin from the

20 t ha�1, which appears normal if there was no firewood

harvesting (Fig. 3), to as little as 3 t ha�1 if firewood was

harvested from coarse woody debris at the maximum

possible sustainable rate.

However, since the maximum sustainable yield of firewood

harvest from coarse woody debris far exceeds the present

demand, there would be no need to harvest coarse woody

debris from all the 12.3 M ha of forest which were considered

suitable for this (Fig. 2a, Table 1). Harvests could involve

removal of rather less than all the firewood available, perhaps

with advantage to biodiversity maintenance. In any case,

much of the forest of the Basin would be unavailable for

firewood harvest, simply because the owner wished to use it

for some other purpose. Nor is it likely that the maximum

sustainable yield could ever be achieved. It would be

ARTICLE IN PRESS


impossible to insist that each and every forest property be

managed with the particular harvest management regime

that is necessary to achieve the maximum yield. As well,

wood of some tree species is much preferred for firewood over

others [4], which would exclude some from consideration for

harvesting.

It was estimated that a maximum annual supply of

2.3 M t yr�1 of firewood could be sustained by harvesting live

trees by thinning principal forest types and clear-felling

mallee forests. This is about equal to the present annual

demand for firewood from the Basin. For the same reasons as

those for coarse woody debris collection, it is unlikely that all

of the 9.8 M ha of forests considered suitable for live tree

harvests (Fig. 2b, Table 1) would be available and neither

would the maximum supply ever be achieved. That is to say,

live tree harvests would not be able to replace entirely coarse

woody debris collection to supply existing firewood demand.

An important advantage of live tree harvesting is that coarse

woody debris is retained in the forests (Fig. 3), with possible

advantage to biodiversity maintenance.

Acknowledgements

This work was commissioned by the Australian Common-

wealth Department of Environment and Heritage. It was

financed both by them and CSIRO Sustainable Ecosystems.

For assistance with GIS information and advice in this project

we thank D. Barrett, S. Briggs, S. Doyle, M. Howden,

D. Kennedy, A. Langston, P. Nanninga, D. O’Connell, K. Ord,

D. Osborn, J. Seddon and A. Zerger. A. Deane assisted greatly

with discussion of silvicultural management regimes for

forests of the Basin. A large number of individuals assisted

us in identifying suitable field locations from which data were

collected and we thank, particularly, the land owners who

permitted access to their properties. Particular assistance

with equipment and advice for the model development

aspects of this project was given by J. Banks, N. Coops, J.

Fields, N. Huth, I. Mcleod and D. Spencer.

Appendix A

This appendix describes the growth and yield model devel-

oped in the present work for the principal native forests of the

Murray-Darling Basin. The model concentrates on the pre-

diction of firewood yields, either through collection of coarse

woody debris or by thinning live trees from stands. Model

development was based both on data collected from the

forests during this project and on application of some

relevant, pre-existing work.

A.1. Data

Data were collected from a range of the principal forest types,

scattered across the Murray-Darling Basin. These were found

on 23 different properties and a total of 79 stands were

located on those properties. Five stands were dominated by

non-eucalypt species, whilst the remainder were eucalypt

forest types.

In each stand, the species, diameter at breast height (1.3 m)

over bark and total height of each live tree included in a ‘point

sample’ of the stand [21] were measured. In most stands, the

stem wood volume under bark from ground to tip was

measured, using the ‘centroid method’ [21], for each of two

or three of the trees. In total, stem wood volume was

measured for 252 trees.

The stem wood volume data were used to derive an

individual tree volume function, to estimate tree stem wood

volume (V, m3) from diameter at breast height over bark

(D, cm) and tree total height (H, m) as

V ¼ 0:246� 10�4D1:996H0:947. (5)

This model was used to estimate the stem wood volumes of

live trees measured in the point samples, but for which the

stem wood volume had not been measured directly. Stem

wood volumes were converted to stem wood biomasses,

assuming wood basic densities for each species as given in

[22]. These tree stem biomass results were then used to

estimate the stand stem wood biomass from the point sample

for the live trees for each of the 79 stands.

A similar point sampling method was used to determine

the stem wood biomass of standing dead trees in each stand.

Wood density of those trees was assumed to be that of the live

tree species occurring most commonly in the stand.

In 45 of the stands, a 25�50 m2 rectangular plot was

established about the point at which the point sample was

made. Measurements were made of the length and diameter

at mid-length of any piece of fallen woody debris on the

ground, which had a mid-diameter of 10 cm or more and

length of at least 0.5 m [23]. As it was measured, each piece of

woody debris was assigned to one of three classes (1) wood

was solid when kicked and lacked cavities, cracks or a hollow

pipe, (2) mostly solid when kicked but contained cavities,

cracks or a hollow pipe or (3) gave or crushed when kicked.

The volume of each piece of fallen woody debris was

determined using Huber’s formula [21]. Its biomass was then

determined assuming its density was that of the stem wood of

the live tree species occurring most commonly in the stand.

Debris of class 1 was assumed to have suffered negligible

decay and to be of that density. Debris of classes 2 and 3 were

assumed to have suffered some decay and to have densities of

75% and 30%, respectively, of undecayed wood.

In subsequent model development, data for standing dead

trees and fallen woody debris were combined to determine a

total of woody debris for each stand.

Various stand characteristics were measured also. Since the

principal forests of the Basin include both even- and uneven-

aged forest, it is not practical to determine stand age simply

as the age of the trees. Rather, stand age was defined as the

time since a stand regenerated from bare ground following

clearing, destructive wildfire or other natural calamity. Ages

of the 79 stands were determined from records kept by the

property owners.

The productive capacity of a site, that is the rate of growth

of plants on it, depends on the fertility of its soil and its

weather conditions, particularly temperature and rainfall.

Two attempts have been made to map site productive

capacity right across Australia [9,24]. Both used a combination

of satellite imagery of existing vegetation and growth model

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Table 3 – Minimum-mean-maximum values of standcharacteristics determined for principal forest typestands measured in the Murray-Darling Basin

Stand characteristic Minimum–mean–maximum

Age (yr) 10–82–200

NPP index (t ha�1 yr�1) 2–7–13

Live tree stem wood biomass

(t ha�1)

3–54–190

Live tree stocking density

(stems ha�1)

20–2207–39,773

Coarse woody debris (t ha�1) 0–14–82


systems to estimate the maximum annual rate of net primary

production (above- plus below-ground biomass) of plants

anywhere across the continent. This measure of site produc-

tive capacity will be referred to here as ‘NPP index’.

Arbitrarily, it was decided to use the index developed by

Barrett [9]. Dr. Barrett (CSIRO Plant Industry, Australia) made

available to us a GIS surface with the values of his index for all

of Australia, determined with an accuracy to the nearest

5.2�5.2 km2. From this surface, the NPP index for each of the

79 measured stands was determined.

Table 3 lists the minimum–mean–maximum values of the

characteristics determined from these measurements in the

79 stands (or 45 stands in the case of coarse woody debris

measurements).

A.2. Predicting biomass

These data were used to develop a model to predict stand

stem wood biomass of live trees in the stand at any age, to

about 200 yr of age, [BS(T), t ha�1] as

BSðTÞ ¼ 0:852 expf4:854� 0:231Sþ 0:0177S2

� 0:239½lnðrÞ� � 0:0346½lnðrÞ�2

þ 0:949ðS=TÞ þ 10:815½lnðrÞ=T�

þ 12:485½lnðrÞ=T�2g, (6)

where T (yr) is stand age, S (t ha�1 yr�1) is NPP index, ln( � )

denotes natural logarithms and

r ¼ 0:000181S2:71. (7)

Firewood may be obtained from branch wood of live trees as

well as their stem wood. A model to predict branch wood

biomass was devised as follows. The generalised model for

Australian native forests of Snowdon et al. [25] predicts total

above-ground stand biomass of a stand [BT(T), t ha�1] at any

age T (yr) from its stand stem wood biomass (see Fig. 2.3b of

[25], with rearrangement of the function quoted there) as

BTðTÞ ¼ 1:720BSðTÞ0:962. (8)

Unpublished data from Australian forests (J. Knott, pers.

comm.) suggested that stand branch biomass including bark

[BK(T), t ha�1] at any age T is directly proportional to the

difference between total above-ground and stem wood

biomasses and may be predicted as

BKðTÞ ¼ 0:324½BTðTÞ � BSðTÞ�. (9)

Averaging the results of [26] for several eucalypt species of

the Murray-Darling Basin suggested branch wood stand

biomass [BB(T), t ha�1] at any age T could be estimated from

total branch stand biomass as

BBðTÞ ¼ 0:88BKðTÞ. (10)

Using the coarse woody debris data measured here, a model

was developed to predict the stand biomass of coarse woody

debris [BC(T), t ha�1] in an undisturbed stand (that is where

coarse woody debris had not been lost by removal or fire) at

any age T (yr) as

BCðTÞ ¼ 0:437BSðTÞ. (11)

A.3. Predicting dynamics of coarse woody debris biomass

A model was now developed to predict how coarse woody

debris amounts change from year to year in a stand. From this

point on, it was assumed that the model system would be

used at annual time-step intervals.

Suppose the change in the amount of coarse woody debris

in a stand between ages T and T+1 is denoted as DBC(T)

(t ha�1 yr�1). This can be represented easily as

DBCðTÞ ¼ BCðTþ 1Þ � BCðTÞ (12)

However, over any year from T to T+1, it can be recognised

also that the net change in coarse woody debris is made up of

additions (DBC+(T), t yr�1), as live trees shed limbs or die, and

reductions (DBC�(T), t yr�1), as existing coarse woody debris

rots away. Expressions for these changes were assumed to be

DBCþðTÞ ¼ ½BSðTÞ þ BBðTÞ�tWðTÞ, (13a)

and

DBC�ðTÞ ¼ BCðTÞtC, (13b)

where tW(T) (yr�1) is the proportion of stand branch and stem

wood biomass of live trees converted to coarse woody debris

between T and T+1 and tC (yr�1) is the proportion of existing

coarse woody debris lost through decay. Recognising that

DBCðTÞ ¼ DBCþðTÞ � DBC�ðTÞ, (14)

substituting the right-hand sides of Eqs. (12) and (13) into

Eq. (14) and rearranging, leads to

tWðTÞ ¼ fBCðTþ 1Þ � BCðTÞ½1� tC�g=fBSðTÞ þ BBðTÞg. (15)

Thus tW(T) can be determined at any age T, as long as a

value is available for tC.

A review [27] of Australian and world literature on the rate

of decay of coarse woody debris in forest shows it varies

enormously in different types of forest, from as short as 1 yr

to as long as several hundred years. It varies with the size of

the material, with the quality of the wood and its natural

resistance to decay and with the environmental character-

istics of the site, particularly the moisture and temperature

regimes which affect the activity of decay micro-organisms.

However, Barrett [9] determined that it generally takes an

average of about 23 yr for coarse woody debris to decay

completely in tall forests of Australia; the value of tC is the

reciprocal of this, that is, 0.0435 yr�1. This was assumed to be

an appropriate value of tC for the present model.

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A.4. Predicting harvest yields

The models developed above were now used as part of a

complete model system to predict amounts of firewood which

can be harvested by collecting coarse woody debris and/or by

removing live trees by thinning, from stands of the principal

forest types of the Murray-Darling Basin. The complete

system was built and is used in two parts.

Consider a stand growing on a site of a particular

productive capacity (NPP index) in the Basin. The first part

of the model system involves prediction of the stand biomass

of the stem and branch wood of living trees and coarse woody

debris annually for each year of the life of the stand, from 1 to

200 yr (or such shorter time as is desired), assuming there is

no loss of wood from a stand during its life (through firewood

harvest by thinning or coarse woody debris removal, fire

passing through it or any other wood removal), other than by

normal decay of coarse woody debris. This is done using

models (6)–(11). As well, values for the rate of conversion of

live tree stem and branch wood to coarse woody debris [tW(T)]

are determined, for all but the last year, using model (15).

The second part of the model system uses these results and

certain other assumptions, which are described below, to

predict the amounts of firewood which can be harvested from

this stand from time to time during its life. At the same time,

an account is kept of the stand branch and stem wood of live

trees and of the coarse woody debris which remain in the

stand year by year as harvesting continues. The user will need

to specify when harvests are to be done, what types of

harvests are to be done (thinning and/or coarse woody debris

removal) and what proportion of the available biomass is to

be removed at each harvest.

In the second part of the model system, a new set of

symbols will be used to represent the stand biomasses of the

live trees and coarse woody debris which remain in the stand

at any age. These will be the same symbols as used above,

except that a prime (0) will be appended to the symbol.

Suppose the model user specifies that, at some age T (yr), a

firewood harvest is done by considering for harvest some

proportion, C(T), of the coarse woody debris biomass then

present in the stand. Not all that coarse woody debris

biomass will be of a size large enough to be used for firewood.

In a study of the firewood industry on part of the eastern

boundary of the Murray-Darling Basin, [26] found that 82% of

biomass harvested for firewood was large enough to be sold

as firewood. Thus, a harvest of coarse woody debris for

firewood will involve removal of an amount B0CFðTÞ (t ha�1) of

the coarse woody debris of the stand, where,

B0CFðTÞ ¼ 0:82CðTÞB0CðTÞ, (16)

where B0CðTÞ (t ha�1) is the biomass of coarse woody debris in

the stand at age T immediately before the harvest. Immedi-

ately this harvest is done, that amount of coarse woody debris

is deducted from B0CðTÞ to give the new amount then

remaining in the stand. Until a firewood harvest is done,

either by thinning live trees or by collecting coarse woody

debris, the values of B0CðTÞ will be the same as the values of

BC(T) from an undisturbed stand.

The amount of coarse woody debris remaining in the stand

in successive years after the harvest is then determined, year

by year, using

B0CðTþ 1Þ ¼ ½B0SðTÞ þ B0BðTÞ�tWðTÞ � B0CðTÞ½1� tC�, (17)

where B0SðTÞ and B0BðTÞ (t ha�1) are the stem and branch wood

stand biomasses of live trees present in the stand at age T and

tW(T) was determined using model (15). Between ages T and

T+1, this model makes additions to the coarse woody debris

from deaths of, or branch shedding by, live trees and

subtractions by decay of existing debris, consistent with

model (13). If the value determined by model (17) is less than

zero, then B0CðTþ 1Þ is set to zero before calculating coarse

woody debris amounts for a subsequent year.

Firewood may be obtained also by harvesting live trees from

a stand, that is by thinning the stand. Suppose the model user

specifies that, at some age (T, yr) a thinning is to be done

which involves removal of some proportion, L(T), of the live

tree wood biomass of the stand; the number of trees actually

removed in such a harvest will depend on the relative sizes of

the trees chosen to be thinned. Thus, an amount B0LFðTÞ

(t ha�1) of firewood would be obtained at the thinning, where,

B0LFðTÞ ¼ 0:82LðTÞ½B0SðTÞ þ B0BðTÞ�, (18)

where B0SðTÞ and B0BðTÞ are the stand wood biomasses of stems

and branches, respectively, of live trees present in the stand

at the time of thinning and it is assumed that 82% of the

harvested biomass will be saleable as firewood, as assumed

for model (16). Immediately the thinning is done, biomass

amounts LðTÞB0SðTÞ and LðTÞB0BðTÞ will be deducted from B0SðTÞ

and B0BðTÞ, respectively, to give their new amounts then

remaining in the stand. Until the first thinning is done,

B0SðTÞ and B0BðTÞ will have the same values as BS(T) and BB(T),

respectively, as determined for the undisturbed stand in the

first part of the model.

To determine subsequent growth of the live trees in a

thinned stand, it was assumed that the total above-ground

biomass production to any age of a thinned stand (that is the

above-ground biomass of the live trees in the stand at that

age, plus the total amount of coarse woody debris that had

been produced up to that age, plus the total amount of live

tree biomass which had been removed from the stand by

thinning up to that age) was the same as the total above-

ground biomass production of the corresponding unthinned

stand to the same age. This assumes that, despite the

immediate loss of foliage biomass from a stand due to

thinning, the photosynthetic capacity of the remaining trees

will increase to just balance the loss. Eventually the trees

remaining after thinning will expand their canopies so that

production by the thinned stand continues to be the same as

if it was unthinned. The validity of this assumption can

judged from various works. This concept, that total produc-

tion by thinned and unthinned stands is the same, has

developed from research undertaken in plantation and highly

productive native forests in various parts of the world [28], but

remains untested for the rather slow growing forests of the

Murray-Darling Basin. However, in the absence of any other

information for the Basin, it seemed a reasonable assumption

to make here.

To apply this assumption, the total above-ground stand

biomass which has been removed from a stand by thinning,

at any age up to and including age T, B0(T) (t ha�1) is

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determined as

B0ðTÞ ¼X

I¼1...TB0LFðIÞ

h i=0:82. (19)

As well, model (13a) is used to determine the cumulative

amount of stand biomass of coarse woody debris that has

been produced up to age T+1 both by the thinned stand

[B0CTðTÞ, t ha�1] and by the corresponding unthinned stand

[BCT(T), t ha�1] as

B0CTðTÞ ¼X

I¼1...T½B0SðIÞ þ B0BðIÞ�tWðIÞ� �

, (20a)

and

BCTðTÞ ¼X

I¼1...T½BSðIÞ þ BBðIÞ�tWðIÞ� �

. (20b)

Assuming then that total production by thinned and

unthinned stands is the same, it follows that, before any

thinning is done at age T+1,

B0TðTþ 1Þ þ B0ðTÞ þ B0CTðTÞ ¼ BTðTþ 1Þ þ BCTðTÞ. (21)

This model can be rearranged to determine the above-

ground stand biomass of the live trees in a thinned stand at

age T+1 as

B0TðTþ 1Þ ¼ BTðTþ 1Þ þ BCTðTÞ � B0ðTÞ � B0CTðTÞ. (22)

Rearrangements of models (8) and (9) can then be used to

convert this total above-ground biomass to stand stem and

Fig. 4 – Scatter plot of the observed stand stem wood

biomasses of live trees (t ha�1), in the 79 stands measured in

the Murray-Darling Basin, against their values predicted by

the model system developed here, assuming each stand

had been undisturbed by thinning during its lifetime. The

solid line shows where the plotted points would lie if there

was exact agreement between the observed and predicted

values.

branch wood biomasses [B0SðTþ 1Þ and B0BðTþ 1Þ, respectively].

To apply this system successfully, it must be assumed that

the first thinning is done at some age after 1 yr of age.

If models (17) and (22) are used in concert year by year, the

model system will keep track of the stand biomasses of live

trees and of coarse woody debris remaining in a stand at any

year, when firewood is being harvested by removing coarse

woody debris and/or by thinning live trees. The amounts of

stand wood biomass harvested for firewood at any of these

harvests will be given by models (16) and (18).

A.5. Testing and applying the model

Formal testing of this model system would require informa-

tion on firewood harvest yields obtained from a large number

of stands in the Murray-Darling Basin which had varying

histories of disturbance over their lifetimes. No such com-

prehensive data set was available here. However, Fig. 4 shows

a scatter plot of the observed stand stem wood biomasses

against values predicted by the model for the 79 stands

measured here, assuming each stand had been undisturbed

by thinning, up to the age at which it was measured. There is

Fig. 5 – Predictions from the model system of the change

with age in the amounts of stand stem plus bark wood

biomass in live trees (—), stand coarse woody debris (- - -)

and the cumulative stand biomass of firewood harvested

(— - —) in a stand where firewood was harvested both by

collecting coarse woody debris and by felling live trees. The

simulated stand was assumed to be growing on a site with

an NPP index of 12 t ha�1 yr�1, which is quite a high

productive capacity for the Murray-Darling Basin. Thinnings

were done at 55 and 105 yr of age, at each of which 50% of

the biomass of the live trees was removed. Coarse woody

debris was collected for firewood every 10 yr, between 20

and 150 yr of age, with all the coarse woody debris of a size

suitable for firewood being collected at each harvest.

ARTICLE IN PRESS


little indication in the results of Fig. 4 of any marked bias in

stand stem wood live tree biomass prediction, except perhaps

a tendency to underestimate biomasses at higher levels of

biomass; however, the data are insufficient to judge this

adequately.

Using methods of [29], the information in Fig. 4 shows that

the 95% confidence limit about predictions made with the

model of live tree stand stem wood biomass of a single

stand in the Basin is 7153% of the predicted value. This is a

very low precision of estimate, probably too low to be

useful practically. However, if the model is used to predict

the average stand stem wood biomass of stands of a

particular site productive capacity across a wide area of the

Basin, the 95% confidence limit about the predicted average

would be 717% of the predicted value, a far more acceptable

precision of estimate. In the present work, the model was

used only to make predictions of average yields across large

areas.

Unfortunately, insufficient data were available here from

undisturbed stands to undertake a test similar to that of Fig. 4

for coarse woody debris in the measured stands.

As an example of the model in use, Fig. 5 illustrates results

when predicting growth and firewood yields for a stand from

which firewood was harvested both by thinning live trees and

by collecting coarse woody debris. The loss of biomass of live

trees and of coarse woody debris as each harvest was done is

obvious.

The model system developed here should be considered

only as a first approximation to a growth and yield model for

the principal forest types of the Murray-Darling Basin. It was

based on a limited collection of data from only 79 forest

stands, insufficient to sample adequately the complete range

of forest types which occur across the Basin. It then used a

number of other assumptions derived from reports in the

literature, often based on forest types other than those of the

Basin. These limitations reflect the lack of research interest in

the past for forests of the Basin, in turn reflecting the little

commercial use that has been made of them. It will require a

very substantial research effort either to validate fully and/or

develop further this model system.

R E F E R E N C E S

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firewood harvest from forests of the murray-darling basin, australia. part 1: long-term, sustainable...

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